DISCONTINUITY-INDUCED MIXED MODE OSCILLATIONS FOR THE NONSMOOTH MURALI–LAKSHMANAN–CHUA CIRCUIT

We present a detailed investigation into the occurrence of complex patterns in the memristive Murali– Lakshmanan–Chua (MLC) circuit system. The nonsmooth system is divided into fast and slow subsystems by assuming a cosinusoidal function as a slow variable. The determination of the region of bifurcation space in the fast subsystem (the FS) is associated with nonsmooth boundaries and switching manifolds. The transition through the switching boundaries may give rise to complicated dynamics including coexistence of bilateral equilibrium states and jumping behaviors constituting the relaxation-type oscillation cycles. Combined with the generalized Jacobian matrix and Clarke derivative, discontinuous bifurcations of the fast subsystem at the nonsmooth boundaries are investigated. Two types of oscillation modes are obtained, and their generating mechanism is discussed. It is revealed that not only the equilibrium dynamics of the fast subsystem but also discontinuous bifurcations at switching boundaries have a deep impact on the whole system dynamic, leading to the sudden transition on two switching boundaries. Finally, performance of this nonlinear nonsmooth MLC circuit system is well verified by numerical simulations and analytical studies © 2023 MSP (Mathematical Sciences Publishers)